How to access driver f-curve data with python?
I was trying to use keyframe_insert(), but what I needed to use was keyframe_points.add().

Here is a sample that adds a F-Curve with an ease-in and ease-out to the driver:

import bpy

context = bpy.context
data = bpy.data
aobj = context.active_object
me = aobj.data
scn = context.scene
objs = data.objects

if me.shape_keys == None:
    bpy.ops.object.shape_key_add(from_mix=False)

bpy.ops.object.shape_key_add(from_mix=False)

current_key = me.shape_keys.key_blocks[1]

sk = me.shape_keys
cur_key = sk.key_blocks[1]
cur_key.driver_add('value', -1)
drivers = sk.animation_data.drivers

cur_driver = drivers[0]
cur_driver.modifiers.remove(cur_driver.modifiers[0])

cur_driver.keyframe_points.add()
cur_driver.keyframe_points.add()

co = [(0.0, 0.0), (1.0, 1.0)]
handles = [[(-0.25, 0.0), (0.25, 0.0)],[(0.75, 1.0), (1.25,1.0)]]
for i in range(len(co)):
    cur_driver.keyframe_points[i].co = co[i]
    cur_driver.keyframe_points[i].handle_left_type = 'FREE'
    cur_driver.keyframe_points[i].handle_right_type = 'FREE'
    cur_driver.keyframe_points[i].handle_left = handles[i][0]
    cur_driver.keyframe_points[i].handle_right = handles[i][1]